Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.4% → 96.6%

Time: 6.2s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{y}{y - z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ y (- y z))))

C

double code(double x, double y, double z) {
	return x / (y / (y - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (y / (y - z))
end function

Java

public static double code(double x, double y, double z) {
	return x / (y / (y - z));
}

Python

def code(x, y, z):
	return x / (y / (y - z))

Julia

function code(x, y, z)
	return Float64(x / Float64(y / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x / (y / (y - z));
end

Wolfram

code[x_, y_, z_] := N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.1%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

3. Simplified 98.2%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
4. Add Preprocessing

5. Final simplification 98.2%

   \[\leadsto \frac{x}{\frac{y}{y - z}} \]
6. Add Preprocessing

Alternative 2: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000135 \lor \neg \left(z \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.000135) (not (<= z 1.25e-23))) (* x (/ (- z) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.000135) || !(z <= 1.25e-23)) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.000135d0)) .or. (.not. (z <= 1.25d-23))) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.000135) || !(z <= 1.25e-23)) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.000135) or not (z <= 1.25e-23):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.000135) || !(z <= 1.25e-23))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.000135) || ~((z <= 1.25e-23)))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.000135], N[Not[LessEqual[z, 1.25e-23]], $MachinePrecision]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000002e-4 or 1.2500000000000001e-23 < z

   1. Initial program 86.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 94.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 94.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 67.9%

         \[\leadsto x \cdot \color{blue}{\left(-\frac{z}{y}\right)} \]

      2. distribute-neg-frac 67.9%

         \[\leadsto x \cdot \color{blue}{\frac{-z}{y}} \]

   7. Simplified 67.9%

      \[\leadsto x \cdot \color{blue}{\frac{-z}{y}} \]

   if -1.35000000000000002e-4 < z < 1.2500000000000001e-23

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000135 \lor \neg \left(z \leq 1.25 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.000135 \lor \neg \left(z \leq 1.28 \cdot 10^{-23}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.000135) (not (<= z 1.28e-23))) (* z (/ (- x) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.000135) || !(z <= 1.28e-23)) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.000135d0)) .or. (.not. (z <= 1.28d-23))) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.000135) || !(z <= 1.28e-23)) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.000135) or not (z <= 1.28e-23):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.000135) || !(z <= 1.28e-23))
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.000135) || ~((z <= 1.28e-23)))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.000135], N[Not[LessEqual[z, 1.28e-23]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000002e-4 or 1.28000000000000005e-23 < z

   1. Initial program 86.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 94.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 94.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 68.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} \]

      2. mul-1-neg 68.9%

         \[\leadsto \frac{\color{blue}{-x \cdot z}}{y} \]

      3. distribute-rgt-neg-out 68.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{y} \]

      4. associate-*l/ 69.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-z\right)} \]

   7. Simplified 69.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-z\right)} \]

   if -1.35000000000000002e-4 < z < 1.28000000000000005e-23

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000135 \lor \neg \left(z \leq 1.28 \cdot 10^{-23}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.9e-5) (/ x (/ (- y) z)) (if (<= z 7.2e-24) x (* z (/ (- x) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e-5) {
		tmp = x / (-y / z);
	} else if (z <= 7.2e-24) {
		tmp = x;
	} else {
		tmp = z * (-x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.9d-5)) then
        tmp = x / (-y / z)
    else if (z <= 7.2d-24) then
        tmp = x
    else
        tmp = z * (-x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.9e-5) {
		tmp = x / (-y / z);
	} else if (z <= 7.2e-24) {
		tmp = x;
	} else {
		tmp = z * (-x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.9e-5:
		tmp = x / (-y / z)
	elif z <= 7.2e-24:
		tmp = x
	else:
		tmp = z * (-x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.9e-5)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (z <= 7.2e-24)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(-x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.9e-5)
		tmp = x / (-y / z);
	elseif (z <= 7.2e-24)
		tmp = x;
	else
		tmp = z * (-x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.9e-5], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-24], x, N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8999999999999998e-5

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.1%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{y}{z}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 71.1%

         \[\leadsto \frac{x}{\color{blue}{\frac{-1 \cdot y}{z}}} \]

      2. neg-mul-1 71.1%

         \[\leadsto \frac{x}{\frac{\color{blue}{-y}}{z}} \]

   7. Simplified 71.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{-y}{z}}} \]

   if -5.8999999999999998e-5 < z < 7.2000000000000002e-24

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.0%

      \[\leadsto \color{blue}{x} \]

   if 7.2000000000000002e-24 < z

   1. Initial program 90.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 90.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 91.6%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 91.6%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 71.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{y}} \]

      2. mul-1-neg 71.7%

         \[\leadsto \frac{\color{blue}{-x \cdot z}}{y} \]

      3. distribute-rgt-neg-out 71.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{y} \]

      4. associate-*l/ 69.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-z\right)} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.2e-5) (/ x (/ (- y) z)) (if (<= z 1.8e-24) x (/ (* x (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-5) {
		tmp = x / (-y / z);
	} else if (z <= 1.8e-24) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.2d-5)) then
        tmp = x / (-y / z)
    else if (z <= 1.8d-24) then
        tmp = x
    else
        tmp = (x * -z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e-5) {
		tmp = x / (-y / z);
	} else if (z <= 1.8e-24) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.2e-5:
		tmp = x / (-y / z)
	elif z <= 1.8e-24:
		tmp = x
	else:
		tmp = (x * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.2e-5)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (z <= 1.8e-24)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.2e-5)
		tmp = x / (-y / z);
	elseif (z <= 1.8e-24)
		tmp = x;
	else
		tmp = (x * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.2e-5], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-24], x, N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000027e-5

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.1%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{y}{z}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 71.1%

         \[\leadsto \frac{x}{\color{blue}{\frac{-1 \cdot y}{z}}} \]

      2. neg-mul-1 71.1%

         \[\leadsto \frac{x}{\frac{\color{blue}{-y}}{z}} \]

   7. Simplified 71.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{-y}{z}}} \]

   if -6.20000000000000027e-5 < z < 1.8e-24

   1. Initial program 83.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. *-commutative 83.3%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

      3. *-commutative 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.0%

      \[\leadsto \color{blue}{x} \]

   if 1.8e-24 < z

   1. Initial program 90.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{y} \]
   4. Step-by-step derivation

      1. mul-1-neg 71.7%

         \[\leadsto \frac{\color{blue}{-x \cdot z}}{y} \]

      2. distribute-rgt-neg-out 71.7%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{y} \]

   5. Simplified 71.7%

      \[\leadsto \frac{\color{blue}{x \cdot \left(-z\right)}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (/ (- y z) y)))

C

double code(double x, double y, double z) {
	return x * ((y - z) / y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * ((y - z) / y)
end function

Java

public static double code(double x, double y, double z) {
	return x * ((y - z) / y);
}

Python

def code(x, y, z):
	return x * ((y - z) / y)

Julia

function code(x, y, z)
	return Float64(x * Float64(Float64(y - z) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * ((y - z) / y);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.1%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. *-commutative 85.1%

      \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

   2. associate-*l/ 97.3%

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   3. *-commutative 97.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

3. Simplified 97.3%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
4. Add Preprocessing

5. Final simplification 97.3%

   \[\leadsto x \cdot \frac{y - z}{y} \]
6. Add Preprocessing

Alternative 7: 50.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 85.1%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. *-commutative 85.1%

      \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{y} \]

   2. associate-*l/ 97.3%

      \[\leadsto \color{blue}{\frac{y - z}{y} \cdot x} \]

   3. *-commutative 97.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]

3. Simplified 97.3%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 53.0%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 53.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))